# ode02 - Separable and linear equations: some problems...

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First Prev Next Last Go Back Full Screen Close Quit Separable and linear equations: some problems September 18, 2008

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First Prev Next Last Go Back Full Screen Close Quit Separable equations are among the very simple types of ODE’s for which we can easily recognize and ﬁnd the solutions. Knowing how to compute the integrals ,then you can solve this type of ODE. Separable equations has the form ,or equivalent form, like this g ( y ) dy = f ( x ) dx . The general solution is give by Z g ( y ) dy = Z f ( x ) dx , and if there is an initial value y ( x 0 ) = y 0 , the solution is obtained by taking Z y y 0 g ( y ) dy = Z x x 0 f ( x ) dx . Note that the above procedure gives the solution in a implicit form in some cases. Another point is that there may be some particular solutions which we would likely omit when doing some transforms of the equations. 1.Solve
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## ode02 - Separable and linear equations: some problems...

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